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Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface

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arxiv 2404.11489 v3 pith:GL272MZ7 submitted 2024-04-17 math.NT

Cameron Wilson This is my paper · ORCID
classification math.NT
keywords quadricasymptoticsdiagonalsplitsquaresurfacedensityeverywhere
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abstract

We prove asymptotics for the density of everywhere locally soluble diagonal quadric surfaces parameterised by rational points on the split quadric surface $y_0y_1=y_2y_3$ which do not satisfy $-y_0y_1=\square$ nor $-y_0y_3=\square$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An improved large sieve for quadratic characters via Hooley neutralisers and its applications

    math.NT 2025-06 conditional novelty 7.0 of 10

    Using Hooley neutralisers, a large sieve for quadratic characters is improved for multiplicatively weighted sequences, with applications to hyperbolic-region character sums.

  2. Solubility of a family of conics with polynomial coefficients in many variables

    math.NT 2025-11 reject novelty 6.0 of 10

    An asymptotic for the density of soluble conics with polynomial coefficients is proposed, but the sign decomposition (6.5) that bridges the circle-method counts to the true count is false.

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